Question

How do you find the projection of u onto v given `u=<2,2>` and `<v=6,1>`?

Answer 1

The vector projection of `vecu` onto `vecv` `=〈84/37,14/37〉`

Explanation:

The vector projection of `vecu` over `vecv` is given by
`=(vecu.vecv)/(∣vecv∣^2)vecv`

Dot product `vecu.vecv=〈u_1,u_2〉.〈v_1,v_2〉=u_1v_1+u_2v_2`
The dot product `vecu.vecv=〈2,2〉.〈6,1〉=12+2=14`

`∣vecv∣^2=〈v_1,v_2〉〈v_1,v_2〉=v_1^2+v_2^2`
So `∣vecv∣^2=〈6,1〉〈6,1〉=36+1=37`

And finally the projection is `=14/37〈6,1〉=〈84/37,14/37〉`